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Recursionhard
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Solve the recurrence an=2an−1+1a_n = 2a_{n-1} + 1an​=2an−1​+1 with a0=0a_0 = 0a0​=0 using generating functions. If A(x)=∑n=0∞anxnA(x) = \sum_{n=0}^{\infty} a_n x^nA(x)=∑n=0∞​an​xn, which of the following is the correct generating function A(x)A(x)A(x)?